How to do early classification of time series event with small dataset?
One kind of system you could look into are Echo State Networks (ESNs).
They are relatively cheap to train and can learn to predict output signals to an  arbitrary degree of precision.
All you need to train the system is some labeled training data.
Thus, if you have a sequence of measurements/feature values and the corresponding sequence of class labels, you can train and fine-tune these kinds of systems to output some required class label very quickly after the onset of an event encoded in the measured feature values.